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Wang, Ding Huai; Zhou, Jiang; Teng, Zhi Dong
Acta mathematica Sinica. English series, 08/2021, Letnik: 37, Številka: 8Journal Article
In this paper, we prove that the weighted BMO space BMO p ( ω ) = { f ∈ L loc 1 : sup Q ‖ χ Q ‖ L p ( ω ) − 1 ‖ ( f − f Q ) ω − 1 χ Q ‖ L p ( ω ) < ∞ } is independent of the scale p ∈ (0, ∞) in sense of norm when ω ∈ A 1 . Moreover, we can replace L p ( ω ) by L p ,∞ ( ω ). As an application, we characterize this space by the boundedness of the bilinear commutators b, T j ( j = 1, 2), generated by the bilinear convolution type Calderón-Zygmund operators and the symbol b , from L p 1 ( ω ) × L p 2 ( ω ) to L p ( ω 1− p ) with 1 < p 1 , p 2 < ∞ and 1/ p =1/ p 1 + 1/ p 2 . Thus we answer the open problem proposed by Chaffee affirmatively.
